Functions

Indicate all the diagrams that are functions.

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What statements are correct for a function?

• A function has only one input

• An input can have different output

• A function map one input to only one output

• All input has an output

• Input is an element in Domain and output is an element in Co-domain

Which statement is correct about the diagram.

• It is a relation, but not a function because there is a negative number in the domain

• It is neither relation nor a function

• It is a relation and a function

• It is a relation, but not a function because 11 has two outputs

• It is a not relation, but a function

Which set of values are a function?

• {(9,5),(10,5), (9,-5), (10,-5)}

• {(3,4), (4,-3), (7,4), (3, 8)}

• {(6,-5), (7, -3),(8, -1), (9, 1)}

• {(2, -2), (5, 9), (5, -7), (1, 4)}

• {(6,-5), (7, -3), (8, -1), (9, 1), (6,-1)}

Which graphs are functions?

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Define functions f and g from R to R by the following
formulas: For every x in R,  $f(x)\ =\ 2x$  and  $g(x)\ =\ \frac{2x^3+2x}{x^2+1}$ . Which statement is correct?

•  $f\left(x\right)=g\left(x\right)$  because the domain and co-domain are euqal

•  $f\left(x\right)\ne g\left(x\right)$  because the domain are not equal

•  $f\left(x\right)\ne g\left(x\right)$  because the the co-domain are not equal

•  $f\left(x\right)=g\left(x\right)$  because for every x, f(x) = g(x)

Define a function f : Z+ -> Z+ as follows: For

each positive integer n, f(n) = the sum of all of the positive divisors of n. What is f(15)?

• 1

• 3

• 5

• 15

• 24

Define a boolean function f: {0,1} -> {0,1}, f(x,y,z) = (2x-y+z) mod 2. What is f(2,6,1)?

• -1

• 0

• 1

• Undefined

Consider F. Which statements are correct?

• F is one-to-one

• F is onto

• F is not a function

• None of the answers

Consider H. Which statement is true?

• H is one-to-one

• H is onto

• H is not a function

• None of the answers